Lecture Notes in Mathematics: With Applications to Harmonic Maps of Riemann Surfaces

Burstall, Francis E.; Rawnsley, John H.

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.

Details

Published by: Springer

Publication Date: 1990-05-22

Format: Paperback

ISBN-13: 9783540526025

DOI: 10.1007/BFb0095561

Dimensions: 235cm x155cm

Pages: 110